As the V for Vivala mask can force item drops on critical hits, equipping this in a spare accessory slot could increase your chances. Note that this prevents your opponent from dropping the same item normally that combat.

Hobo Power can currently be raised to a maximum of 170 points (giving a maximum item drop bonus of 85% on Hodgman offhand items).

Other Crown of Thrones/Buddy Bjorn choices exist, which give item drop bonuses to specific categories of items (e.g. Slimeling gives +15% weapon drops). These are not included in the table in the interest of brevity.